A149532 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 0, 0), (-1, 0, 1), (0, -1, 0), (1, 1, 0)}

1, 1, 5, 13, 49, 177, 645, 2489, 9621, 37389, 149641, 595069, 2401449, 9767733, 39781097, 163511229, 674229217, 2789228345, 11601713781, 48355166633, 202230993541, 848452552753, 3566524103253, 15033723662041, 63503474794893, 268735010971945, 1139627242648765, 4840572436506129

Offset

0,3

Links

Table of n, a(n) for n=0..27.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A138277 A343549 A084601 * A149533 A149534 A149535

Adjacent sequences: A149529 A149530 A149531 * A149533 A149534 A149535

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved